Effect of free volume

When a polymer is cooled to 0 K no motion of the groups or constituents is possible. As the temperature is increased from OK the specific volume of the polymer increases (Fig. 1.10). Since there is very little change in the bond lengths with temperature the observed increases in the specific volume must be due to the formation of small holes or voids in the system which collectively increases in size and/or number as the temperature rises. These holes or voids constitute free-volume in the polymer, which is indicated in Fig. 1.10 by the area lying above the straight line parallel to the temperature axis. As the free volume in the polymer increases, various types of molecular motion 

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The asymmetry is easily explained by consideration of the effect of free volume on T. Equilibration at a low temperature produces a low free volume after an increase in temperature, the process of volume dilation is therefore sluggish until the free volume has expanded, and the rate of dilation then accelerates autocatalytically. The reverse occurs after a downward jump in temperature the rate of volume shrinkage slows as the free volume collapses. Similar phenomena occur when the pressure, rather than the temperature, is increased or decreased (Ferry 1980). 

Effect of Free Volume of the Polymer on Diffusion of Hydrocarbons in the Polymer.240... 

Maximizing the content of azo chromophore usually enhances SRG formation (Fukuda et ah, 2000a), although some studies have found that intermediate functionalization (50%-80%) created the largest SRG (Borger et ah, 2005 Andruzzi et ah, 1999). Some attempts have been made to probe the effect of free volume. By attaching substituents to the azo-ring, its steric bulk is increased. 

Robertson, R. E., Effect of free volume fluctuations on polymer relaxation in the glassy state J. Polym. Sci. Polym. Phys. Ed, 17, 597-613 (1979). 

Dlubek, G., Shaikh, M. Q., Krause-Rehberg, R., and Paluch, M., The effect of free volume and temperature on the structural relaxation in polymethylphenylsiloxane a positron lifetime and pressure-volume-temperature study, J. Chem. Phys., 126,024906—1 to 024906—12 (2007a). 

The effect of free volume on penetrant diffusion coefficients in polymers is often described using concepts from the Cohen and Turnbull model (7. This statistical mechanics model provides a simplistic description of diffusion in a liquid of hard spheres. A hard sphere penetrant is considered to be trapped in a virtual cage created by its neighbors. Free volume is defined as the volume of the cage less the volume of the penetrant. Free volume fluctuations, which occur randomly due to thermally-stimulated Brownian motion of neighboring hard spheres, provide opportunities for the penetrant to execute a diffusion step if the gap (i,e, free volume fluctuation) occurs sufficiently close to the i netrant to be accessible and is of sufficient size to acconunodate it. The diffusion coefficient of a penetrant is given by ... 

Figures 6b and 6c present the effect of free volume on methane difrusivity and permeability, respectively. Over the range of free volume explored (0.1 FFV. 16), diffusivity decreases by roughly two orders of magnitude as free volume decreases. The change in permeability with increasing free volume essentially mirrors that of diffusivity, indicating that the most important effect of free volume on transport properties in this family of materials is the impact of free volume on diffusion coefficients.

V. Shantarovich, I. Kevdina, Yu. Yampolskii, A. Alentiev, Positron annihilation lifetime study of high and low free volume glassy polymers effects of free volume size on the permeability and permselectivity. Macromolecules, 33, 7453-7466 (2000). 

Two types of cteviation from the first-orda kinetics are noted for photo-aialthamal isomerization reactions in polymer films. The first is the normal type, in which the reaction rate is the same as or smaller than that in solutions at the initial stage and then progressively becomes smaller. Typical examples are thermal decoloration of the photocolored merocyanine form of spirobenzopyran molecularly dispersed in or chemically bound to a polymer matrix > and photoisomerization of the transazobenzene residue incorporated in polymer main chains The first interpretation for the decoloration of the merocyanine form assumed the existence of different isomers, each of which fades independently following first-order kinetics On the other hand, Kryszewski et al. proposed the kinetic matrix effect, which means that the distribution of free volume may lead to the deviation from first-order kinetics. His idea was based on the finding that deviations from first-order kinetics can be observol even in simple molecules such as azobenzene which has only one trans or cis isomeric form. The effect of free volume distribution on reactivity was further demonstrated by studies of annealed polymer films The distribution function of free volume as well as the critical free volume v were estimated for the merocyanine form of spiropyran in poly(methyl methacrylate) derivatives of azobenzene in polystyrene and azobenzene in polycarbonate The deviation from first-order kinetics was also observed in cyclizing imidization of model poly(amic acid) in a polyamide matrix... 

The temperature depaidence of fdiotoisomerization in polymer solids yields detailed information about the effects of free volume distribution and molecular motion on the reaction process. The present authors measured the rate of trans -+ cis photoisomerization of azobenzene in a polycarbonate film over a very wide range of temperatures (4 K-423 K), and proposed a kinetic model, which consists of chemically... 

Kundu S, Roy SS, Pal Majumder T, Roy SK (2000) Spontaneous polarization and response time of a polymer dispersed ferroelectric liquid crystal (PDFLC). Ferroelectrics 243 197-206 Lahiri T, Pal Majumder T (2011) Theoretical approach to study the effect of free volumes on the physical behavior of polymer stabilized ferroelectric liquid crystal molecules. J Appl Phys 109 114109... 

Evidently, such factors as the delayed rotation of particles in liquid, solvation of reactants and transition state reflect this ratio. Situations are possible where the liquid medium impedes the bimolecular act, and the reaction in gas occurs more promptly than in liquid. However, in all cases, the effect of free volume is rained, which as if accelerates the bimolecular act. This effect should also take place in strongly compressed gases where the substance density proaches that of liquid. 

Robertson, R.E. (1978) Effect of free-volume fluctuations on polymer relaxation inthe glassy state. J. Potym. So. Polym. Symp., 63, 173. 

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